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arxiv: 1503.00224 · v4 · pith:REUSCWHWnew · submitted 2015-03-01 · 🧮 math.QA · math.RA· math.RT

Cellular structures using U_q-tilting modules

Henning Haahr Andersen , Catharina Stroppel , Daniel Tubbenhauer This is my paper
classification 🧮 math.QA math.RAmath.RT
keywords algebrascellularmodulestextbfbasescentralizergeneraltilting
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We use the theory of $\textbf{U}_q$-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group $\textbf{U}_q$ attached to a Cartan matrix and include the non-semisimple cases for $q$ being a root of unity and ground fields of positive characteristic. Our approach also generalizes to certain categories containing infinite-dimensional modules. As applications, we give a new semisimplicty criterion for centralizer algebras, and recover the cellularity of several known algebras (with partially new cellular bases) which all fit into our general setup.

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